Abstract
We consider shortest paths on time-dependent multimodal transportation networks in which restrictions or preferences on the use of certain modes of transportation may arise. We model restrictions and preferences by means of regular languages. Methods for solving the corresponding problem (called the regular language constrained shortest path problem) already exist. We propose a new algorithm, called State Dependent ALT (SDALT), which runs considerably faster in many scenarios. Speed-up magnitude depends on the type of constraints. We present different versions of SDALT, including unidirectional and bidirectional search. We also provide extensive experimental results on realistic multimodal transportation networks.
- Christoper L. Barrett, Keith R. Bisset, Martin Holzer, Goran Konjevod, Madhav Marathe, and Dorothea Wagner. 2008. Engineering label-constrained shortest-path algorithms. In Algorithmic Aspects in Information and Management, Rudolph Fleischer and Jinhui Xu (Eds.). Lecture Notes in Computer Science, Vol. 5034. Springer, Berlin, 27--37. DOI: http://dx.doi.org/10.1007/978-3-540-68880-8_5 Google ScholarDigital Library
- Christoper L. Barrett, Keith R. Bisset, Riko Jacob, Goran Konjevod, and M. V. Marath. 2002. Classical and contemporary shortest path problems in road networks: Implementation and experimental analysis of the TRANSIMS router. In European Symposium on Algorithms (ESA’02)(LNCS), Rolf H. Mohring and Rajeev Raman (Eds.). Lecture Notes in Computer Science, Vol. 2461. Springer, Berlin, 126--138. DOI: http://dx.doi.org/10.1007/3-540-45749-6_15 Google ScholarDigital Library
- Christoper L. Barrett, Riko Jacob, and Madhav Marathe. 2000. Formal-language-constrained path problems. SIAM Journal on Computing 30, 3 (2000), 809--837. DOI: http://dx.doi.org/10.1137/S0097539798337716 Google ScholarDigital Library
- Reinhard Bauer, Daniel Delling, Peter Sanders, Dennis Schieferdecker, Dominik Schultes, and Dorothea Wagner. 2010. Combining hierarchical and goal-directed speed-up techniques for Dijkstra’s algorithm. Journal of Experimental Algorithmics 15, Article 2.3, 2 pages. DOI: http://dx.doi.org/10.1145/1671970.1671976 Google ScholarDigital Library
- Daniel Delling, Andrew V. Goldberg, Thomas Pajor, and Renato Fonseca F. Werneck. 2011. Customizable route planning. In Symposium on Experimental Algorithms (SEA’11), Panos M. Pardalos and Steffen Rebennack (Eds.). Lecture Notes in Computer Science, Vol. 6630. Springer, Berlin, 376--387. DOI: http://dx.doi.org/10.1007/978-3-642-20662-7_32 Google ScholarDigital Library
- Daniel Delling and Giacomo Nannicini. 2008. Bidirectional core-based routing in dynamic time-dependent road networks. In International Symposium on Algorithms and Computation (ISAAC’08), Seok-Hee Hong, Hiroshi Nagamochi, and Takuro Fukunaga (Eds.). Lecture Notes in Computer Science, Vol. 5369. Springer, Berlin, 812--823. DOI: http://dx.doi.org/10.1007/978-3-540-92182-0_71 Google ScholarDigital Library
- Daniel Delling, Thomas Pajor, and Dorothea Wagner. 2009a. Accelerating multi-modal route planning by access-nodes. In European Symposium on Algorithms (ESA’09), Amos Fiat and Peter Sanders (Eds.). Lecture Notes in Computer Science, Vol. 5757. Springer, Berlin, 587--598. DOI: http://dx.doi.org/10.1007/978-3-642-04128-0_53Google ScholarCross Ref
- Daniel Delling, Peter Sanders, Dominik Schultes, and Dorothea Wagner. 2009b. Engineering route planning algorithms. In Algorithmics of Large and Complex Networks, Jurgen Lerner, Dorothea Wagner, and Katharina Anna Zweig (Eds.). Lecture Notes in Computer Science, Vol. 5515. Springer, Berlin, 117--139. DOI: http://dx.doi.org/10.1007/978-3-642-02094-0_7 Google ScholarDigital Library
- Daniel Delling and Dorothea Wagner. 2009. Time-dependent route planning. In Robust and Online Large-Scale Optimization, Ravindra K. Ahuja, Rolf H. Mohring, and Christos D. Zaroliagis (Eds.). Lecture Notes in Computer Science, Vol. 5868. Springer, Berlin, 207--230. DOI: http://dx.doi.org/10. 1007/978-3-642-05465-5_8 Google ScholarDigital Library
- Julian Dibbelt, Thomas Pajor, and Dorothea Wagner. 2012. User-constrained multi-modal route planning. In Algorithm Engineering and Experiments (ALENEX’12), David A. Bader and Petra Mutzel (Eds.). SIAM, Philadelphia, PA, 118--129. http://i11www.iti.uni-karlsruhe.de/extra/publications/dpw-ucmmr-12.pdf.Google Scholar
- E. W. Dijkstra. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 1, 269--271. DOI: http://dx.doi.org/10.1007/BF01386390 Google ScholarDigital Library
- Andrew V. Goldberg and C. Harrelson. 2005. Computing the shortest path: A* search meets graph theory. In Proceedings of the Symposium on Discrete Algorithms (SODA’05). SIAM, Philadelphia, PA, 156--165. Google ScholarDigital Library
- Andrew V. Goldberg and Renato Fonseca F. Werneck. 2005. Computing point-to-point shortest paths from external memory. In ALENEX/ANALCO, Camil Demetrescu, Robert Sedgewick, and Roberto Tamassia (Eds.). SIAM, Philadelphia, PA, 26--40.Google Scholar
- Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. 1968. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics 4, 2, 100--107. DOI: http://dx.doi.org/10.1109/TSSC.1968.300136Google ScholarCross Ref
- Takahiro Ikeda, Min-Yao Hsu, Hiroshi Imai, S. Nishimura, H. Shimoura, T. Hashimoto, K. Tenmoku, and K. Mitoh. 1994. A fast algorithm for finding better routes by AI search techniques. In Proceedings of Vehicle Navigation and Information Systems Conference. IEEE, 291--296. DOI: http://dx.doi.org/10.1109/VNIS.1994.396824Google Scholar
- E. Kaufman and Robert L. Smith. 1993. Fastest paths in time-dependent networks for intelligent vehicle-highway systems applications. IVHS Journal 1, 1 1--11. DOI: http://dx.doi.org/10.1080/10248079308903779Google Scholar
- Dominik Kirchler, Leo Liberti, Thomas Pajor, and Roberto Wolfler Calvo. 2011. UniALT for regular language constrained shortest paths on a multi-modal transportation network. In Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS’11) (OASICS), Alberto Caprara and Spyros C. Kontogiannis (Eds.), Vol. 20. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Germany, 64--75. DOI: http://dx.doi.org/10.4230/OASIcs.ATMOS.2011.64Google Scholar
- Dominik Kirchler, Leo Liberti, and Roberto Wolfler Calvo. 2012. A label correcting algorithm for the shortest path problem on a multi-modal route network. In Symposium on Experimental Algorithms (SEA’12), Ralf Klasing (Ed.). Lecture Notes in Computer Science, Vol. 7276. Springer, Berlin, 236--247. Google ScholarDigital Library
- Angelica Lozano and Giovanni Storchi. 2001. Shortest viable path algorithm in multimodal networks. Transportation Research Part A 35, 225--241. DOI: http://dx.doi.org/10.1016/S0965-8564(99)00056-7Google ScholarCross Ref
- Alberto O. Mendelzon and Peter T. Wood. 1995. Finding regular simple paths in graph databases. SIAM Journal on Computing. 24, 6, 1235--1258. DOI: http://dx.doi.org/10.1137/S009753979122370X Google ScholarDigital Library
- Giacomo Nannicini, Daniel Delling, Leo Liberti, and Dominik Schultes. 2008. Bidirectional A* search for time-dependent fast paths. In Conference on Experimental Algorithms (WEA’08), Catherine C. McGeoch (Ed.). Lecture Notes in Computer Sciencem Vol. 5038. Springer, Berlin, 334--346. DOI: http://dx.doi.org/10.1007/978-3-540-68552-4_25 Google ScholarDigital Library
- Ariel Orda and Raphael Rom. 1990. Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. Journal of the ACM 37, 3, 607--625. DOI: http://dx.doi.org/10.1145/79147.214078 Google ScholarDigital Library
- Ira Pohl. 1971. Bi-directional Search. In Machine Intelligence 6, Bernard Meltzer and Donald Michie (Eds.). Vol. 6. Edinburgh University Press, Edinburgh, 127--140.Google Scholar
- Evangelia Pyrga, Frank Schulz, Dorothea Wagner, and Christos D. Zaroliagis. 2007. Efficient models for timetable information in public transportation systems. ACM Journal of Experimental Algorithmics 12. DOI: http://dx.doi.org/10.1145/1227161.1227166 Google ScholarDigital Library
- Michael Rice and Vassilis J. Tsotras. 2010. Graph indexing of road networks for shortest path queries with label restrictions. Proceedings of the VLDB Endowment 4, 2, 69--80. Google ScholarDigital Library
- J. F. Romeuf. 1988. Shortest path under rational constraint. Information Processing Letters 28, 5, 245--248. Google ScholarDigital Library
- Hanif D. Sherali, Antoine G. Hobeika, and Sasikul Kangwalklai. 2003. Time-dependent, label-constrained shortest path problems with applications. Transportation Science 37, 3, 278--293. Google ScholarDigital Library
- Hanif D. Sherali, Chawalit Jeenanunta, and Antoine G. Hobeika. 2006. The approach-dependent, time-dependent, label-constrained shortest path problem. Networks 48, 2, 57--67. DOI: http://dx.doi.org/10. 1002/net Google ScholarDigital Library
- Mihalis Yannakakis. 1990. Graph-theoretic methods in database theory. In Proceedings of Symposium on Principles of Database Systems. ACM, New York, NY, 230--242. DOI: http://dx.doi.org/10.1145/298514.298576 Google ScholarDigital Library
Index Terms
- Efficient Computation of Shortest Paths in Time-Dependent Multi-Modal Networks
Recommendations
Finding the K shortest paths in a time-schedule network with constraints on arcs
We study a new variant of the time-constrained shortest path problem (TCSPP), that is, the K shortest paths problem in a time-schedule network with constraints on arcs. In such networks, each arc has a list of pre-specified departure times, and ...
Shortest paths in piecewise continuous time-dependent networks
We consider a shortest path problem, where the travel times on the arcs may vary with time and waiting at any node is allowed. Simple adaptations of the Dijkstra algorithm may fail to solve the problem, when discontinuities exist. We propose a new ...
On shortest disjoint paths in planar graphs
For a graph G and a collection of vertex pairs {(s"1,t"1),...,(s"k,t"k)}, the k disjoint paths problem is to find k vertex-disjoint paths P"1,...,P"k, where P"i is a path from s"i to t"i for each i=1,...,k. In the corresponding optimization problem, the ...
Comments